Select tab Ticket Search at the top of Indexed Search form.
In this advance ticket search you can beside define a time filter for last update time similar to the general search, see above, also add extra filter for Ticket Type, Agent Group, Requester Organization and Category. In respective field you can select none, one or multiple types, groups, etc.
You can also in checkboxes define if search shall be performed in open and/or closed tickets and you can delimit search to only tickets having tasks connected. If checkbox Has tasks is enabled you search only for tickets having at least one task, if not enabled search is in all tickets.